A new deformation of multiple zeta value
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911935761481728 |
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| author | Takeyama, Yoshihiro |
| author_facet | Takeyama, Yoshihiro |
| contents | We introduce a new deformation of multiple zeta value (MZV). It has one parameter $ω$ satisfying $0<ω<2$ and recovers MZV in the limit as $ω\to +0$. It is defined in the same algebraic framework as a $q$-analogue of multiple zeta value ($q$MZV) by using a multiple integral. We prove that our deformed multiple zeta value satisfies the double shuffle relations which are satisfied by $q$MZVs. We also prove the extended double Ohno relations, which are proved for ($q$)MZVs by Hirose, Sato and Seki, by using a multiple integral whose integrand contains the hyperbolic gamma function due to Ruijsenaars. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19641 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A new deformation of multiple zeta value Takeyama, Yoshihiro Number Theory Quantum Algebra We introduce a new deformation of multiple zeta value (MZV). It has one parameter $ω$ satisfying $0<ω<2$ and recovers MZV in the limit as $ω\to +0$. It is defined in the same algebraic framework as a $q$-analogue of multiple zeta value ($q$MZV) by using a multiple integral. We prove that our deformed multiple zeta value satisfies the double shuffle relations which are satisfied by $q$MZVs. We also prove the extended double Ohno relations, which are proved for ($q$)MZVs by Hirose, Sato and Seki, by using a multiple integral whose integrand contains the hyperbolic gamma function due to Ruijsenaars. |
| title | A new deformation of multiple zeta value |
| topic | Number Theory Quantum Algebra |
| url | https://arxiv.org/abs/2406.19641 |